The stability parameters of three-dimensional periodic three-body orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear isoenergetic stability parameters of three-dimensional periodic orbits of the general three-boy problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The conditions for stability, criticality, and bifurcations are briefly examined and the stability determination procedure is tested in the determination of some three-dimensional periodic orbits of low inclination bifurcating from vertical-critical coplanar orbits.     

A spectroscopic study of the microorganism model of interstellar grains

The microorganism model of interstellar grains is investigated by spectroscopy from the infrared (IR), visible to the ultraviolet (UV) wave regions.E. coli, yeast and spores ofBacillus subtilis exhibit absorption bands at =3.1 and 9.7 m; they also exhibit several absorptions at 68 m which are in agreement with the observed IS extinction curves.To obtain the extinction curves in the visible and UV regions, dry films of microorganism are prepared on a MgF₂ plate or synthesized quartz plate and their spectra measured. In the wavelength region 190400 nm, conventional spectrophotometers are adopted for the measurement. The extinction curve of the film ofE. coli is similar to the observed IS curve.For the wave-range 100<<400 nm, a vacuum UV spectrometer is adopted to avoid absorptions due to O₂ in the atmosphere. The extinction spectra by this method are in agreement with the result obtained by the conventional method where comparison is possible. The extinction curves ofE. coli and yeast are such that they incrase towards the short wavelength and exhibit a peak at -190 nm, which is different from the well-known IS peak at =220 nm. It remains to be seen whether interstellar low temperatures (1040 K) can shift the peak position in the extinction curve of biochemical materials.     

Development of a real-time algorithm for detection of solar wind discontinuities

A study is presented of an algorithm, based on the statistical analysis of interplanetary magnetic field data, for the real-time detection of discontinuities in the solar wind. The analysis is based on the application of a sliding or searching algorithm together with a minimum variance treatment. A demonstration is given for a Pioneer data set from 29 August, 1966. This particular data set was chosen because it has been extensively studied (in terms of the fast forward MHD shock wave) by previous groups who utilized the three-dimensional Rankine-Hugoniot shock equations after identifying the shock on a subjective basis. Our procedure differs in that it is perfectly objective because of its searching technique. For this particular data set we identify the original shock with excellent agreement with the earlier studies of its normal vector, as well as an additional shock and tangential discontinuity, neither of which had been identified previously.     

Converging magnetogasdynamic cylindrical shock waves in a uniform atmosphere

A self-similar solution to the problem of the implosion of a cylindrical shock wave in the presence of a magnetic field has been investigated. A strong shock wave in a cylindrically-symmetric flow travels to the axis of symmetry through a gas of uniform initial density ₀ and zero-pressure. A comparative study has been made between the results obtained in ordinary gasdynamics and magnetogasdynamics with transverse and axial components of the magnetic field. The value of similarity exponent has been assigned from that found in the paper of Whitham (1958).     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

Nuclear reactions on accreting neutron star surface

The production of X-rays and gamma-rays in bursts is believed to be due to the rapid burning of matter accreted onto a neutron star surface from its companion, most probably a giant star. The accreted matter consists mainly of hydrogen and helium and a very small amount of heavy elements. Due to the infall of matter, the temperature at the bottom layers is raised to a value of the order of 10⁸ K. The neutron star surface density is>10⁷ g cm^–3. As hydrogen burning is a slow process under any temperature and density conditions, we consider the helium-burning reactions as the source of gamma-rays in the neutron star surface. Under high-density conditions the ordinary laboratory reaction rates should become modified. At high-density conditions, the strong screening effect due to the polarising cloud of electrons around the ions become important and enhances the reaction rates considerably. The helium-burning reactions are calculated under such conditions. The abundances of helium-burning products such as¹²C, 1¹⁶O, and²⁰Ne, etc., are computed. Under high-density and temperature conditions carbon is found to be more abundant than oxygen. Neon is completely absent in almost all the relevant physical conditions in which a strong screening effect is operative. It is suggested that explosive burning of accreted helium of 10^–13 M will account for the observed energy of gamm-ray burst.     

Hydrodynamical models of type II supernovae

A series of hydrodynamical models of type-II supernova outbursts (SNII) has been calculated. Approximate relations connecting the total outburst energy ε, the mass of envelope ejectedM, the presupernova radiusR, and the amount of ionizing quanta radiated by the supernovaeN _H with such values as the duration of the light curve plateau Δt, and absolute magnitude in the wavelength bandV and photospheric velocityU _PH observed near the middle of the plateau have been established. Advantage has been taken of the relations to obtain a preliminary evaluation for the characteristics of the average SN II: ε=7×10⁵⁰ erg,M=6M _⊙,R=500R _⊙,N _H=2×10⁵⁸. The SNIIs with plateau-like light curves seem to be accounted for by thermonuclear explosions of degenerate cores of red giant stars and result in a total disruption of the star without any stellar remnant. To the contrary, SNIIs with linear light curves have substantially different properties (in particular, they throw considerably less massive envelopes off). These SNII must signify the birth of collapsed objects—neutron stars (pulsars) or black holes.     

Preliminary observations of solar radio sources with the Culgoora radioheliograph operating at four frequencies

The Culgoora radioheliograph has been modified for observing at 327.4 MHz, which is in addition to the three frequencies (43.25, 80, and 160 MHz) previously available. At the new frequency the array beamwidth is 56, which represents the highest resolution yet available for metre-wavelength solar mapping.At 327.4 MHz the sources of radio emission are mainly in the lowest layers of the corona. Some preliminary four-frequency observations have been made of type I storms. It is found that the source size generally decreases with increasing observing frequency. This result confirms earlier suggestions that the sources of both type I and type III emission are contained in structures whose boundaries diverge outwards in the corona.     

Silica phase transformations in the petroliferous sequences

The joint evolution of organic matter and silica in petroliferous sequences is considered in the terms of the laws of transformation of dispersion systems. The dispersion systems are transformed under conditions of low-temperature solid-phase processes accompanied by the silica phase transition and dehydration that favors the evolution of organic matter.     

The WRF model performance for the simulation of heavy precipitating events over Ahmedabad during August 2006

The summer monsoon season of the year 2006 was highlighted by an unprecedented number of monsoon lows over the central and the western parts of India, particularly giving widespread rainfall over Gujarat and Rajasthan. Ahmedabad had received 540.2mm of rainfall in the month of August 2006 against the climatological mean of 219.8mm. The two spells of very heavy rainfall of 108.4mm and 97.7mm were recorded on 8 and 12 August 2006 respectively. Due to meteorological complexities involved in replicating the rainfall occurrences over a region, the Weather Research and Forecast (WRF-ARW version) modeling system with two different cumulus schemes in a nested configuration is chosen for simulating these events. The spatial distributions of large-scale circulation and moisture fields have been simulated reasonably well in this model, though there are some spatial biases in the simulated rainfall pattern. The rainfall amount over Ahmedabad has been underestimated by both the cumulus parameterization schemes. The quantitative validation of the simulated rainfall is done by calculating the categorical skill scores like frequency bias, threat scores (TS) and equitable threat scores (ETS). In this case the KF scheme has outperformed the GD scheme for the low precipitation threshold.